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Product partition is the problem of partitioning a set of integers into two sets with the same product (rather than the same sum). This problem is strongly NP-hard. [14] Kovalyov and Pesch [15] discuss a generic approach to proving NP-hardness of partition-type problems.
In number theory and combinatorics, a partition of a non-negative integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same partition. (If order matters, the sum becomes a composition.)
The 4-partition problem is a variant in which S contains n = 4 m integers, the sum of all integers is , and the goal is to partition it into m quadruplets, all with a sum of T. It can be assumed that each integer is strictly between T /5 and T /3.
The partition problem - a special case of multiway number partitioning in which the number of subsets is 2. The 3-partition problem - a different and harder problem, in which the number of subsets is not considered a fixed parameter, but is determined by the input (the number of sets is the number of integers divided by 3).
The input to the problem is a set of n items of different sizes, and two integers m, k. The output is a partition of the items into m subsets, such that the number of items in each subset is at most k. Subject to this, it is required that the sums of sizes in the m subsets are as similar as possible.
partition of a matrix; see block matrix, and partition of the sum of squares in statistics problems, especially in the analysis of variance , quotition and partition , two ways of viewing the operation of division of integers.
Memory partition, a memory management technique; Partition (database), the division of a logical database; Logical partition, a subset of a computer's resources, virtualized as a separate computer; Binary space partitioning, in computer science; Partition problem, in number theory and computer science
Typically, graph partition problems fall under the category of NP-hard problems. Solutions to these problems are generally derived using heuristics and approximation algorithms. [ 3 ] However, uniform graph partitioning or a balanced graph partition problem can be shown to be NP-complete to approximate within any finite factor. [ 1 ]